Glacial landscapes are sculpted by the combined actions of ice and water. Whereas ice masses with basal water presence typically imprint linear scouring marks on the landscape, glacial landscapes may also consist of channels that merge to produce sub-glacial rivers, with little trace of scouring marks. These sub-glacial channels make the drainage system of ice caps. On Mars, the scarcity of scoured landscapes has led many to consider that water rarely existed under Martian ice masses. However, a fraction of the Martian valleys displays characteristics that are more consistent with erosion in sub-glacial channels than in rivers.  My work identifies subglacial channels among the Martian valleys using analogue fieldwork, numerical modeling, and statistical methods. As a Marie Curie Fellow, I will also interrogate the role of the smaller surface gravity in the drainage of Martian ice sheets by using models of water drainage under terrestrial ice. As a consequence of a feedback mechanism, subglacial channels should form readily and develop much more easily on Mars than Earth, favoring glacial landscapes consisting of channels and their depositional remains, eskers.